Regular star molecules

Fig. 17. Reciprocal partide-scattering factors of regular star-molecules (f = 1 represents the monodisperse linear chain)88, ...

Finally we mention the Kratky plot which also may help to detect branching. Here ((S2) q2) Pz (q2) is plotted against q. Figures 26 and 27 show the Kratky plots for regular star-molecules and for the soft sphere model. Linear randomly coiled chains result in... 

Fig. 40. Relative deviation of the first eumulant in the hydrodynamic pre-average approximation from the correct first eumulant for regular star-molecules of various ray numbers82 ...

Fig. 51. Increase of the coefficient C with molecular polydispersity for linear chains (left) and decrease of C with branching for regular star molecules (right)101 predicted by theory...

Again, this structure resembles very much a linear chain, when the side chains are much shorter than the backbone. The other limit is that of a short backbone and long side chains grafted on the backbone in the densest way. This structure will approach the behavior of star molecules. It should be mentioned that a realization of complete regularity will scarcely be possible. It is almost im-... 

Fig. 2. Two limiting cases of a regular comb molecule. The flexible chain sections between two branching points may consist of m monomer units while the/flexible side chains have a length of n monomer units. The one structure (short side chains) resembles a substituted linear chain, the second one (short backbone) has similarity to star molecules...

Expansions of the forms of Eqs. (6.1) and (6.6) hold also for branched polymers, though the numerical values of the coefficients are different, and depend on the type of branching. The coefficient al has been obtained (25) for regular star and symmetrical comb structures it is found that for these at is greater than the value 134/105 for linear polymers. This implies that as the temperature is increased above T= , branched molecules expand more rapidly than linear ones, so that for T> 0, g> g0. For molecules having many short branches on a long backbone, as the number of branches increases at approaches a limit ... 

For flexible regular-star branched molecules with / identical arms (/ random-flight chains starting from a common node), P(q) is given by (10,1 1)... 

The book also covers the solution properties of the regular star polymers. This class of materials has been known for many years to polymer chemists however, rapid development has occurred only ce tiie proposal of the idea of dendritic polymers in the mid-1980s. The characteristics of tiie polymers discussed here include the size and shape of the molecules, their biological activities, their low viscosity in solution, their substrate-holding properties inside the molecule, etc. The unique properties of these polymers attract many chemists, not only in polymer chemistiy but also in organic chemistry, biochemistry, medicine, oiganometaUic chemistry, catalyst chemistry, and so on, for these new materials are e q)ected to find applications in many... 

Among many types of branched polymers, star polymers have the simplest stmeture with only one branching point in each molecule. The chains connected to the branching point are usually called the arms. If we use the living polymerization technique, we can obtain regular star polymers having a fixed number of arms with equal length. ... 

Under certain conditions, rather well-defined ring and honeycomb patterns can be formed by solution casting of thin films. Recently Nolte described the formation of isolated rings with diameters of several micrometers formed by stacked porphyrin molecules [287], Phase segregation or eruption of gas bubbles was assumed to be responsible for the peculiar assembly of the porphyrin wheels . However, the regular shape of the solute molecules was also considered to be of crucial importance, Another example is the honeycomb pattern of star shaped poly(styrene)-block-poly(-p-phenylene) films described by Francois [288], In this case, the peculiar molecular shape was emphasized to be of crucial importance besides the proper choice of solvent and evaporation conditions [289],... 

The name dendrimer refers to the star- or tree-shaped, branched structures of this relatively new class of cationic gene transfer systems [8, 78-81]. They are frequently synthesized from polyami-doamines with special chemical or physical features. Probably best known are the starburst dendrimers with particle sizes ranging from 5 to 100 nm. These particles reveal a highly regular branched dendritic symmetry. Starburst dendrimers are three-dimensional oligomeric or polymeric compounds, which, initiated from small molecules as nuclei, are built layer-by-layer ( generations ) by repeated... 

In conclusion, let us recall that until now the canonical labels have been used on individual molecules. This is the first time that the canonical labels have been constructed for a family of molecules, if one disregards trivial cases path graphs, mono-cyclic graphs, and star graphs. Hence, in this chapter, not only have we introduced the novelty of ring closure matrices, but we have opened a new topic in the field of canonical labels concerned with regularities of the canonical labels for families of structurally related molecules. 

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